Unique expectations for discrete crossed products

Abstract

Let $G$ be a discrete group acting on a unital $C^{\ast }$-algebra $\mathcal{A}$ by $\ast$-automorphisms. We characterize (in terms of the dynamics) when the inclusion $\mathcal{A}\subseteq \mathcal{A}{⋊}_{r}G$ has a unique conditional expectation, and when it has a unique pseudo-expectation (in the sense of Pitts). Likewise for the inclusion $\mathcal{A}\subseteq \mathcal{A}⋊G$. As an application, we (slightly) strengthen results of Kishimoto and Archbold-Spielberg concerning $C^{\ast }$-simplicity of $\mathcal{A}{⋊}_{r}G$.

References in corpus (1)

• A Galois correspondence for reduced crossed products of unital simple C${}^{\ast }$-algebras by discrete groups

Cited by in corpus (4)

• Noncommutative boundaries and the ideal structure of reduced crossed products
• Aperiodicity: the almost extension property and uniqueness of pseudo-expectations
• The pure extension property for discrete crossed products
• Free coactions of a finite dimensional $C^{\ast }$-Hopf algebra and strong Morita equivalence